/*
 * Copyright (c) 2015 Typelevel
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
 * COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
 * IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

package cats
package laws

/**
 * Laws that must be obeyed by any `cats.MonoidK`.
 */
trait MonoidKLaws[F[_]] extends SemigroupKLaws[F] {
  implicit override def F: MonoidK[F]

  def monoidKLeftIdentity[A](a: F[A]): IsEq[F[A]] =
    F.combineK(F.empty, a) <-> a

  def monoidKRightIdentity[A](a: F[A]): IsEq[F[A]] =
    F.combineK(a, F.empty) <-> a

  def repeatK0[A](x: F[A]): IsEq[F[A]] =
    F.combineNK(x, 0) <-> F.empty

  def collectK0[A](x: A): IsEq[F[A]] =
    F.combineAllK(Nil) <-> F.empty

  def combineAllK[A](xs: Vector[F[A]]): IsEq[F[A]] =
    F.combineAllK(xs) <-> (F.empty[A] +: xs).reduce(F.combineK[A])

  def isId[A](x: F[A], eqv: Eq[F[A]]): IsEq[Boolean] =
    eqv.eqv(x, F.empty) <-> F.isEmpty(x)(eqv)
}

object MonoidKLaws {
  def apply[F[_]](implicit ev: MonoidK[F]): MonoidKLaws[F] =
    new MonoidKLaws[F] { def F: MonoidK[F] = ev }
}
